endure in techniques this form of the equation of a airplane. we've 3 unknowns in the final sort. z=ax+by using+c the place a, b, and c are constants. we've 3 factors, so we are able to write 3 equations to unravel for a,b and c factors are (-a million/2,0,0), (0,-4/3,0), and (0,0,-5/8) shall we write those equations a million) 0=-a million/2a+0b+c 2) 0=0a-4/3b+c 3) -5/8=0a+0b+c from 3) all of us be attentive to that c=-5/8 Plug this cost right into a million) and a pair of) and resolve for a and b respectively. 0=-a million/2 a - 5/8 a=-10/8=-5/4 0=-4/3b - 5/8 b=-15/32 the airplane is z= -5/4 a - 15/32 b - 5/8
Comments
x^2 = y + z, y^2 = z + x, z^2 = x + y
or,x^2+x=y+z+x, y^2+y=z+x+y, z^2+z=x+y+z
i.e,x(x+1)=x+y+z, y(y+1)=x+y+z, z(z+1)=x+y+z ...(i)
Now,
(1/x+1) + (1/y+1) + (1/z+1)
=1/(x+1) + 1/(y+1) + 1/(z+1)
=x/[x(x+1)] + y/[y(y+1)] + z/[z(z+1)]
=x/(x+y+z) + y/(x+y+z) + z/(x+y+z) ( using (i) )
=(x+y+z)/(x+y+z) ( on simplifying )
=1 ( <= Answer)
x^2 = y + z, y^2 = z + x, z^2 = x + y
The above three equalities are of similar
nature and can be true only if x = y = z
=>x^2 = x + x
=>x(x - 2) = 0
=>x = 0 and 2
=>x = y = z = 0 and 2
1/x+1 + 1/y+1 + 1/z+1
I) when x=y=z=0
= 1+1+1 = 3
II) when x=y=z=2
= 1/3+1/3+1/3 = 1
If x^2 = y + z, y^2 = z + x, z^2 = x + y
x^2 + y^2 + z^2 = 2(x + y + z)
(1/x+1) + (1/y+1) + (1/z+1) = 9/2
endure in techniques this form of the equation of a airplane. we've 3 unknowns in the final sort. z=ax+by using+c the place a, b, and c are constants. we've 3 factors, so we are able to write 3 equations to unravel for a,b and c factors are (-a million/2,0,0), (0,-4/3,0), and (0,0,-5/8) shall we write those equations a million) 0=-a million/2a+0b+c 2) 0=0a-4/3b+c 3) -5/8=0a+0b+c from 3) all of us be attentive to that c=-5/8 Plug this cost right into a million) and a pair of) and resolve for a and b respectively. 0=-a million/2 a - 5/8 a=-10/8=-5/4 0=-4/3b - 5/8 b=-15/32 the airplane is z= -5/4 a - 15/32 b - 5/8